Contour

If you were to take a certain elevation threshold (contour line) and select all area ABOVE that line, you might end up with a polygon that is essentially a mountain top. I work for a non-profit organization that works primarily in watersheds but we also work in places like the buffer area surrounding the Mt. Kilimanjaro National Park and the Foret des Pins in Haiti to restore and protect the land, where the project boundary is defined by an elevation threshold (roughly).

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Contour

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contour(Z) creates a contour plot containing the isolines of matrix Z, where Z contains height values on the x-y plane. MATLAB automatically selects the contour lines to display. The column and row indices of Z are the x and y coordinates in the plane, respectively.

contour(___,levels) specifies the contour lines to display as the last argument in any of the previous syntaxes. Specify levels as a scalar value n to display the contour lines at n automatically chosen levels (heights). To draw the contour lines at specific heights, specify levels as a vector of monotonically increasing values. To draw the contours at one height (k), specify levels as a two-element row vector [k k].

contour(___,Name,Value) specifies additional options for the contour plot using one or more name-value pair arguments. Specify the options after all other input arguments. For a list of properties, see Contour Properties.

Contour levels, specified as a scalar whole number or a vector. Use this argument to control the number and location of the contour lines. When you do not specify the levels, the contour function chooses the levels automatically.

Label spacing along the contour lines, specified as a scalar value in points, where one point is 1/72 inch. Use this property to control the number of contour labels along the contour lines. Smaller values produce more labels.

A contour line (also isoline, isopleth, isoquant or isarithm) of a function of two variables is a curve along which the function has a constant value, so that the curve joins points of equal value.[1][2] It is a plane section of the three-dimensional graph of the function f ( x , y ) {\displaystyle f(x,y)} parallel to the ( x , y ) {\displaystyle (x,y)} -plane. More generally, a contour line for a function of two variables is a curve connecting points where the function has the same particular value.[2]

In cartography, a contour line (often just called a "contour") joins points of equal elevation (height) above a given level, such as mean sea level.[3] A contour map is a map illustrated with contour lines, for example a topographic map, which thus shows valleys and hills, and the steepness or gentleness of slopes.[4] The contour interval of a contour map is the difference in elevation between successive contour lines.[5]

The gradient of the function is always perpendicular to the contour lines. When the lines are close together the magnitude of the gradient is large: the variation is steep. A level set is a generalization of a contour line for functions of any number of variables.

Contour lines are curved, straight or a mixture of both lines on a map describing the intersection of a real or hypothetical surface with one or more horizontal planes. The configuration of these contours allows map readers to infer the relative gradient of a parameter and estimate that parameter at specific places. Contour lines may be either traced on a visible three-dimensional model of the surface, as when a photogrammetrist viewing a stereo-model plots elevation contours, or interpolated from the estimated surface elevations, as when a computer program threads contours through a network of observation points of area centroids. In the latter case, the method of interpolation affects the reliability of individual isolines and their portrayal of slope, pits and peaks.[6]

The idea of lines that join points of equal value was rediscovered several times. The oldest known isobath (contour line of constant depth) is found on a map dated 1584 of the river Spaarne, near Haarlem, by Dutchman Pieter Bruinsz.[7] In 1701, Edmond Halley used such lines (isogons) on a chart of magnetic variation.[8] The Dutch engineer Nicholas Cruquius drew the bed of the river Merwede with lines of equal depth (isobaths) at intervals of 1 fathom in 1727, and Philippe Buache used them at 10-fathom intervals on a chart of the English Channel that was prepared in 1737 and published in 1752. Such lines were used to describe a land surface (contour lines) in a map of the Duchy of Modena and Reggio by Domenico Vandelli in 1746, and they were studied theoretically by Ducarla in 1771, and Charles Hutton used them in the Schiehallion experiment. In 1791, a map of France by J. L. Dupain-Triel used contour lines at 20-metre intervals, hachures, spot-heights and a vertical section. In 1801, the chief of the French Corps of Engineers, Haxo, used contour lines at the larger scale of 1:500 on a plan of his projects for Rocca d'Anfo, now in northern Italy, under Napoleon.[9][10][11]

By around 1843, when the Ordnance Survey started to regularly record contour lines in Great Britain and Ireland, they were already in general use in European countries. Isobaths were not routinely used on nautical charts until those of Russia from 1834, and those of Britain from 1838.[9][12][13]

When maps with contour lines became common, the idea spread to other applications. Perhaps the latest to develop are air quality and noise pollution contour maps, which first appeared in the United States in approximately 1970, largely as a result of national legislation requiring spatial delineation of these parameters.

Contour lines are often given specific names beginning with "iso-" according to the nature of the variable being mapped, although in many usages the phrase "contour line" is most commonly used. Specific names are most common in meteorology, where multiple maps with different variables may be viewed simultaneously. The prefix "'iso-" can be replaced with "isallo-" to specify a contour line connecting points where a variable changes at the same rate during a given time period.

An isogon (from Ancient Greek (gonia) 'angle') is a contour line for a variable which measures direction. In meteorology and in geomagnetics, the term isogon has specific meanings which are described below. An isocline (, klinein, 'to lean or slope') is a line joining points with equal slope. In population dynamics and in geomagnetics, the terms isocline and isoclinic line have specific meanings which are described below.

A curve of equidistant points is a set of points all at the same distance from a given point, line, or polyline. In this case the function whose value is being held constant along a contour line is a distance function.

In 1944, John K. Wright proposed that the term isopleth be used for contour lines that depict a variable which cannot be measured at a point, but which instead must be calculated from data collected over an area, as opposed to isometric lines for variables that could be measured at a point; this distinction has since been followed generally.[16][17] An example of an isopleth is population density, which can be calculated by dividing the population of a census district by the surface area of that district. Each calculated value is presumed to be the value of the variable at the centre of the area, and isopleths can then be drawn by a process of interpolation. The idea of an isopleth map can be compared with that of a choropleth map.[18][19]

Meteorological contour lines are based on interpolation of the point data received from weather stations and weather satellites. Weather stations are seldom exactly positioned at a contour line (when they are, this indicates a measurement precisely equal to the value of the contour). Instead, lines are drawn to best approximate the locations of exact values, based on the scattered information points available.

Meteorological contour maps may present collected data such as actual air pressure at a given time, or generalized data such as average pressure over a period of time, or forecast data such as predicted air pressure at some point in the future.

An isobar (from Ancient Greek (baros) 'weight') is a line of equal or constant pressure on a graph, plot, or map; an isopleth or contour line of pressure. More accurately, isobars are lines drawn on a map joining places of equal average atmospheric pressure reduced to sea level for a specified period of time. In meteorology, the barometric pressures shown are reduced to sea level, not the surface pressures at the map locations.[21] The distribution of isobars is closely related to the magnitude and direction of the wind field, and can be used to predict future weather patterns. Isobars are commonly used in television weather reporting.

Contours are one of several common methods used to denote elevation or altitude and depth on maps. From these contours, a sense of the general terrain can be determined. They are used at a variety of scales, from large-scale engineering drawings and architectural plans, through topographic maps and bathymetric charts, up to continental-scale maps. 2351a5e196